Generate all the permutations of a given set.

This can be solved recursively.

{a1} -> a1
{a1, a2} -> {a1, a2}, {a2, a1}
{a1, a2, a3} -> {a1, a2, a3}, {a1, a3, a2}, {a3, a1, a2} , {a2, a1, a3}, {a2, a3, a1}, {a3, a2, a1}

So you can generate f(n) given f(n-1). pretty easy